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Ergodic BSDE with unbounded and multiplicative underlying diffusion and application to large time behaviour of viscosity solution of HJB equation

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  • Hu, Ying
  • Lemonnier, Florian

Abstract

We study ergodic backward stochastic differential equations (EBSDEs), for which the underlying diffusion is assumed to be multiplicative and of linear growth. The fact that the forward process has an unbounded diffusion is balanced with an assumption of weak dissipativity for its drift. Moreover, the forward equation is assumed to be non-degenerate. We study the existence and uniqueness of EBSDEs and we apply our results to an ergodic optimal control problem. In particular, we show the large time behaviour of viscosity solution of Hamilton–Jacobi–Bellman equation with an exponential rate of convergence when the underlying diffusion is multiplicative and unbounded.

Suggested Citation

  • Hu, Ying & Lemonnier, Florian, 2019. "Ergodic BSDE with unbounded and multiplicative underlying diffusion and application to large time behaviour of viscosity solution of HJB equation," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 4009-4050.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:10:p:4009-4050
    DOI: 10.1016/j.spa.2018.11.008
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    References listed on IDEAS

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    1. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    2. Debussche, Arnaud & Hu, Ying & Tessitore, Gianmario, 2011. "Ergodic BSDEs under weak dissipative assumptions," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 407-426, March.
    3. Briand, Ph. & Delyon, B. & Hu, Y. & Pardoux, E. & Stoica, L., 2003. "Lp solutions of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 109-129, November.
    4. Madec, P.Y., 2015. "Ergodic BSDEs and related PDEs with Neumann boundary conditions under weak dissipative assumptions," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1821-1860.
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    Cited by:

    1. Juan Li & Wenqiang Li & Gechun Liang, 2020. "A game theoretical approach to homothetic robust forward investment performance processes in stochastic factor models," Papers 2005.10660, arXiv.org, revised May 2021.

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